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The projective plane over K, denoted PG(2, K) or KP 2, has a set of points consisting of all the 1-dimensional subspaces in K 3. A subset L of the points of PG(2, K ) is a line in PG(2, K ) if there exists a 2-dimensional subspace of K 3 whose set of 1-dimensional subspaces is exactly L .
The Fano plane is the projective plane with the fewest points and lines. The smallest 2-dimensional projective geometry (that with the fewest points) is the Fano plane, which has 3 points on every line, with 7 points and 7 lines in all, having the following collinearities:
In the Cayley plane, lines and points may be defined in a natural way so that it becomes a 2-dimensional projective space, that is, a projective plane. It is a non-Desarguesian plane, where Desargues' theorem does not hold. More precisely, as of 2005, there are two objects called Cayley planes, namely the real and the complex Cayley plane.
In mathematics, a plane is a two-dimensional space or flat surface that extends indefinitely. A plane is the two-dimensional analogue of a point (zero dimensions), a line (one dimension) and three-dimensional space. When working exclusively in two-dimensional Euclidean space, the definite article is used, so the Euclidean plane refers to the ...
One common model of the real projective plane is the space of lines in three-dimensional Euclidean space which pass through a particular origin point; in this model, lines through the origin are considered to be the "points" of the projective plane, and planes through the origin are considered to be the "lines" in the projective plane.
A two-dimensional complex space – such as the two-dimensional complex coordinate space, the complex projective plane, or a complex surface – has two complex dimensions, which can alternately be represented using four real dimensions. A two-dimensional lattice is an infinite grid of points which can be represented using integer coordinates.
Comparison of several types of graphical projection, including elevation and plan views. To render each such picture, a ray of sight (also called a projection line, projection ray or line of sight) towards the object is chosen, which determines on the object various points of interest (for instance, the points that are visible when looking at the object along the ray of sight); those points of ...